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# Electromagnetic Induction 12.1

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IBO HL Topic 12.1

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### Electromagnetic Induction 12.1

1. 1. Electromagnetism Topic 12.1 Electromagnetic Induction
2. 2. Induced Electromotive Force (e.m.f.) What is electromagnetic induction? The diagram shows a copper rod connected to an ammeter: There is no battery in the circuit.
3. 3.  What happens when you move the copper rod downwards, to cut across the horizontal magnetic field? The pointer on the meter makes a brief `flick to the right, showing that an electric current has been induced.
4. 4.  What happens when you move the rod upwards? The meter again gives a `flick, but this time to the left. You have now induced a current in the opposite direction.
5. 5.  If you hold the rod stationary, or if you move the rod along the field lines, there is no induced current.
6. 6. Why does electromagnetic induction occur? When you move the copper rod, its free electrons move with it. But when a charge moves in a magnetic field it experiences a force on it (the B Q v force). You can use Flemings Left hand Rule to show that the force on each electron is to the left as shown in the diagram (Remember that an electron moving down has to be treated like a positive charge moving up.
7. 7.  So electrons accumulate at one end of the rod, making it negative. This leaves the other end short of electrons and therefore positive. There is now a voltage (potential difference) across the ends of the moving rod. If the ends of the moving rod are joined to form a complete circuit, the induced voltage causes a current to flow round the circuit as shown by the flick of the ammeter.
8. 8.  The induced voltage is a source of electrical energy ‑ an e.m.f When a conductor is moving in a magnetic field like this, an e.m.f is induced, even if there isnt a complete circuit for a current to flow.
9. 9. Formula for a Straight Conductor Consider a conductor of length l that moves with velocity v perpendicular to a magnetic flux density or induction B as shown in the figure.
10. 10.  When the wire conductor moves in the magnetic field, the free electrons experience a force because they are caused to move with velocity v as the conductor moves in the field.F = e v B
11. 11.  This force causes the electrons to drift from one end of the conductor to the other, and one end builds‑up an excess of electrons and the other a deficiency of electrons. This means that there is a potential difference or emf between the ends. Eventually, the emf becomes large enough to balance the magnetic force and thus stop electrons from moving.
12. 12.  evB = eE ( from F = evB and F = eE) Therefore E = Bv If the potential difference (emf) between the ends of the conductor is ε then ε = E L (from E = V/d) By substitution we haveε = B v L
13. 13. Magnetic Flux The magnetic flux (Φ) through a region is a measure of the number of lines of magnetic force passing through that region. Φ = AB cos θ where A is the area of the region and θ is the angle of movement between the magnetic field and a line drawn perpendicular to the area swept out. The unit of magnetic flux is the weber Wb.
14. 14.  For a single conductor in the magnetic flux density, it can be seen that ε = - ΔΦ/ Δt (the rate of change of flux density) For N number of conductors as in the case for a solenoid, the term flux‑ linkage is used. Then ε = - N Δ (Φ/ Δt) This is Faraday’s Law The minus sign shows us that the emf is always produced so as to oppose the change in flux.
15. 15. Time-changing Magnetic Flux Therefore the production of an emf is produced by a time changing magnetic flux. This could be due to the wire or coil moving through a magnetic field Or by an increasing or decreasing magnetic field of an electromagnet next to a wire or coil.
16. 16. Faraday’s Law We know that an e.m.f. is induced when there is a change in the flux linking a conductor. Faradays law makes the connection between the size of the induced e.m.f. and the rate at which the flux is changing. It states that: the magnitude of the induced e.m.f is directly proportinonal to the rate of change of magnetic flux or flux linkage.
17. 17. Linking For a single conductor in the magnetic flux density, it can be seen that ε = - ΔΦ/ Δt (the rate of change of flux density) And ε = B v l Therefore - ΔΦ/ Δt = B v l
18. 18. Lenz’s Law Faradays law tells us the size of the induced e.m.f., but we can find its direction using Lenzs law The direction of the induced e.m.f is such that it will try to oppose the change in flux that is producing it.
19. 19.  Lenzs law is illustrated in the diagrams: As you move the N‑pole into the coil, an e.m.f. is induced which drives a current round the circuit as shown. Now use the right‑hand grip rule Can you see that the current produces a magnetic field with a N‑pole at the end of the coil nearest to the magnet? So the coil repels the incoming magnet, and in this way the induced current opposes the change in flux.
20. 20.  Why is the current reversed as you move the N‑pole out? By Lenzs law, the coil needs to attract the receding N‑pole
21. 21.  Lenzs law is a result of the conservation of energy. If you move the magnet into the coil, you feel the repulsive force. You have to do work to move the magnet against this force. And so energy is transferred from you (or the system that is moving the magnet) to the electrical energy of the current.